Parsimony Measures in Multi-objective Genetic Programming for Symbolic Regression

We investigate in this paper the suitability of multi-objective algorithms for Symbolic Regression (SR), where desired properties of parsimony and diversity are explicitly stated as optimization goals. We evaluate different secondary objectives such as length, complexity and diversity on a selection of symbolic regression benchmark problems. Our experiments comparing two multi-objective evolutionary algorithms against standard GP show that multi-objective configurations combining diversity and parsimony objectives provide the best balance of numerical accuracy and model parsimony, allowing practitioners to select suitable models from a diverse set of solutions on the Pareto front.